This is the 9th volume in Avner Friedman's collection of Mathematics in Industrial problems. This book aims to foster interaction between industry and mathematics at the "grass roots" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The topics explored in this volume include diffusion in porous media and in rubber/glass transition, coating flows, solvation of molecules, semiconductor processing, optoelectronics, photographic images, density-functional theory,...

This is the tenth volume in the series "Mathematics in Industrial Prob lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level;" that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists....

This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates...

This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.
The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and...

This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.
The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of...

th Although photography has its beginning in the 17 century, it was only in the 1920 s that photography emerged as a science. And as with other s- ences, mathematics began to play an increasing role in the development of photography. The mathematical models and problems encountered in p- tography span a very broad spectrum, from the molecular level such as the interaction between photons and silver halide grains in image formation, to chemical processing in ?lm development and issues in manufacturing and quality control. In this book we present mathematical models that arise in today s p-...

Thisisthefourthvolumeintheseries TutorialsinMathematicalBiosciences. These lectures are based on material which was presented in tutorials or developed by visitors and postdoctoral fellows of the Mathematical B- sciences Institute (MBI), at The Ohio State University. The aim of this series is to introduce graduate students and researchers with just a little ba- ground in either mathematics or biology to mathematical modeling of biol- ical processes. The ?rst volume was devoted to mathematical neuroscience, which was the focus of the MBI program 2002 2003. The second volume dealt with...

This accessible and self-contained treatment provides even readers previously unacquainted with parabolic and elliptic equations with sufficient background to understand research literature. Author Avner Friedman -- Director of the Mathematical Biosciences Institute at The Ohio State University -- offers a systematic and thorough approach that begins with the main facts of the general theory of second order linear parabolic equations.
Subsequent chapters explore asymptotic behavior of solutions, semi-linear equations and free boundary problems, and the extension of results concerning...

This is the eighth volume in the series "Mathematics in Industrial Prob lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level"; that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists....

The human genome of three billion letters has been sequenced. So have the genomes of thousands of other organisms. With unprecedented resolution, modern technologies are allowing us to peek into the world of genes, biomolecules, and cells - and flooding us with data of immense complexity that we are just barely beginning to understand. A huge gap separates our knowledge of the components of a cell and what is known from our observations of its physiology. The authors have written this graduate textbook to explore what has been done to close this gap of understanding between the realms of...